Find the equation of the tangent line to the graph of the function f(x) = (1,−14). (x²+6) (x − 3) at the point

Q: Find the derivative of the function. f(t) = sin²(esin²(t))

A: The Power Rule:The Chain Rule:

Q: 3. Use the limit definition to calculate the slope of the tangent to the curve f(x) = x² + 3x-5 at…

A: The given curve is

Q: Find the general solution of the given second-order differential equation. + 36y = 0 y(x) = y"

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Q: A kite 40 m above the ground moves horizontally at the rate of 3 m/s. At what rate is the angle…

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Q: Consider a plane with direction vectors  [−2,8,5] and  [5,0,−7]. The plane passes through the point…

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Q: Find the arc length L of the graph of r(t). r(t) = t³ i + 1 j + ½ √61² L = i k, √61² k₂ 3 ≤1 ≤4

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Q: Year, t 9 10 11 12 13 14 Table for 20 Subscribers, S 86.0 109.5 128.4 140.8 158.7 182.1

A: The linear function is in the form .

Q: Solve the given differential equation by undetermined coefficients. y". + 5y' + 4y = 12 y(x) =

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Q: Find a polynomial function of least degree having only real coefficients, a leading coefficient of…

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Q: The position of a particle moving in a straight line during a 5-second trip ( 0 ≤ t ≤ 5) is given by…

A: The velocity function given is

Q: If 7 1/2 yards of varnished cambric (insulation) cost $22, what is its cost per yard

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Q: 28. Differentiate a) f(x) = and SIMPLIFY the following functions: e-3x² cos² (4x-5) b) f(x)= (x-6)¹…

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Q: ind the area of the region enclosed by the curves x=y²-4y and x=2y-y² Area =

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Q: Find the volume of the solid obtained by rotating the region bounded by the given curves about the…

A: To find the  volume of the solid obtained by rotating the region bounded by the given curves about…

Q: Evaluate the following limit sản xẠT SENK sn lim X-3x/2 Select the correct choice below and, if…

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Q: Which set of numbers could be the lengths of the sides of a triangle? A. {3,6,9} B. (6,7,13) OC.…

A: We are required to:

Q: 6 Let F = (e²4, sinº x, cos x). Calculate curl(F). curl(F) =

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Q: Use the intermediate value theorem to show that the polynomial function has a real zero between the…

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: 6. Use a series to evaluate the following definite integral: e-2³ dx

A: We have to evaluate the definite integral

Q: Consider two nonnegative numbers x and y such that x+y=10. Maximize and minimize the quantities.…

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Q: Solve the given differential equation by undetermined coeffic y" - 6y' + 9y = 9x + 7 y(x) =

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: For the following function, one zero is given. Find all other zeros. f(x)=x³-9x² + 25x -25; 2-i C…

A: Solution

Q: Evaluate the following limit. Use l'Hôpital's Rule when it is convenient and applicable. lim 1+- X→∞…

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Q: All boxes with a square base, an open top, and a volume of 220 ft³ have a surface area given by…

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Q: Given that 3 is a zero of the polynomial function f(x), find the remaining zeros. (x)=x³-5x² +23x-51…

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Q: Find the critical points of the functions f (x, y) = x² + 2y² - 4y + 6x, g(x, y) = x² – 10xy + y Use…

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Q: For the polynomial function, use the remainder theorem and synthetic division to find f(k). f(x) =…

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Q: Solve the given differential equation by undetermined coefficients. y"-y'- + y(x) = y = = 7+ex/2

A: The solution is shown in step-2

Q: Find and simplify the derivative of 2²-√xy = 2y² + 3x. Evaluate the derivative at the point (t, t).

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Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

A: The indicated function  is a solution of the given differential equation.By using the reduction of…

Q: lim (1 + ln x)¹/(x−1) x → 1

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Q: Find the second derivative. 16. y = 7x^4 - 4x^2 + 6 17. y = 8 sin x

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Q: Find the indicated partial derivatives. f(x, y) = x³y7 - x7y6; fxxx' fxyx fxxx(x, y) = fxyx(x, y) =…

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Q: Consider the equation below. 2 1 + sin(0) (a) Find the eccentricity. e= r= li

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Q: Find a geometric power series for the function, centered at 0, by the following methods. 8 9-x (a)…

A: For geometric series centered at zero:-

Q: Find the derivative of the function. (6) - cos(6²)

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Q: Find the flux of the field F(x,y,z) = zª i+xj - 6z k outward through the surface cut from the…

A: To find the flux of given field.

Q: Find the maximum and minimum values of the function f(x, y, z)=x+2y subject to the constraints y²…

A: The solution is shown in step-2

Q: Determine the following indefinite integral. Check your work by differentiation. So/³ dr S√₁³ dr =

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Q: Find a homogeneous linear differential equation with constant coefficients whose general solution is…

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Q: 2. A radioactive isotope has a half-life of 7 hours. a. Write an equation to represent the amount of…

A: A radioactive isotope has a half-life of 7 hours.The initial amount of sample is 1800 g

Q: √r +3 6) lim- √r-9 644

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Q: The number of times a new pop song has been downloaded t weeks after its initial release is given…

A: We have to find the time at which there are maximum downloads, then find rate of change and number…

Q: The diagram that has a limit at x = a is

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Q: For the following polynomial, one zero is given. Find the remaining zeros. f(x)=x+27x²-324,- 6i is a…

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Q: Use the Maclaurin series sin x = S sint t Find the first three terms of the Maclaurin series of dt =…

A: The solution is shown in step-2

Q: 3. Fully simplify fully: a. 0 b. 1 (6-2)(6³) 36 6-² d. 6-¹ b. A horizontal translation 2 units right…

A:

Q: 17 A company's marginal cost function is c(x)=- √x Find the total cost of the first 49 units (from…

A: Given marginal cost is we have to find the total cost of the first  49 units.